Normally, coverage for an owned vehicle is primary. However, the other insurance clause in the standard BAP states that liability assumed under an insured contract is primary. So, you need to check if the GC's auto policy applies under an insured contract in this instance; if so, his auto policy will become primary. If the GC does not have an applicable auto policy, then your insured's policy will be primary.

You did not mention any CGL form that might apply, but since a backhoe could be considered mobile equipment by definition and the GC probably has a CGL form, you need to review that policy also for possible coverage. An insured contract under the terms of the CGL form would mean that the GC has assumed the tort liability of your insured and so, the CGL form of the GC would apply primarily. Of course, this relies on the backhoe being considered mobile equipment; if it is considered an auto, the auto exclusion on the CGL form would prevent coverage.